lim (x->0) sin^2 (x/2)/x = | t = x/2; x = 2 * t, x -> 0 => t -> 0 | =
= lim (t->0) sin^2 t/(2 * t) = 1/2 * lim (t->0) sin^2 t/t =
= 1/2 * lim (t->0) sin t * lim (t->0) sin t/t = 1/2 * 0 * 1 = 0.